The present invention relates generally to simulations of ion implanted dopant profiles, and, more particularly, to simulations of ion implanted dopant profiles in semiconductors using molecular dynamics models.
Ions are implanted into semiconductor wafers to dope regions within the semiconductor substrate in order to modify electrical properties of the substrate and thereby create new electronic devices. As used herein, the term ion will be used to refer to an implanted species and the term atom will be used to refer to a particle of the target material; neither term will connote the charge state of either atom type.
As performance demands increase, smaller devices are required with concomitant reduction in the volumes available to provide distinct doped regions. The measurement and modeling of dopant profiles within these ultrashallow junction devices present challenges, as effects that were negligible at high implant energies become increasingly important as the implant energy is lowered. The experimental measurement of dopant profiles by secondary ion mass spectrometry (SIMS) becomes problematic for very low energy (less than 10 keV) implants. There is a limited depth resolution of measured profiles due to profile broadening and mixing as the SIMS ion beam produces xe2x80x9cknock-onsxe2x80x9d and leads to effects such as diffusion of dopants and mixing. The roughness and disorder of the sample surface can also convolute the profile, although this can be avoided to a large extent by careful sample preparation.
The use of computer simulation as a method for studying the effects of ion bombardment of solids is well established. Binary collision approximation (BCA), xe2x80x9cevent-drivenxe2x80x9d codes, have traditionally been used to calculate such properties as ranges of implanted species and the damage distributions resulting from the collision cascade. The BCA approach breaks down at low energies where multiple collisions (where the ion has simultaneous interactions with more than one target atom) or collisions between moving atoms become significant, where the crystal binding energy is of the same order as the energy of the ion, or when the time spent within a collision is too long for the calculation of asymptotic trajectories to be valid. Such problems are clearly evident when one attempts to use the BCA to simulate channeling in semiconductors. Here, the interactions between the ion and the target are neither binary nor collisional in nature; rather they occur as many simultaneous soft interactions that steer the ion down the channel.
An alternative to BCA is to use molecular-dynamics (MD) simulation. Molecular dynamics has long been applied to the investigation of ion bombardment of materials to calculate the ion trajectories. With the increase in computational power, the development of efficient algorithms, and the production of accurate empirical potentials, it is now feasible to conduct realistic MD simulations.
In the classical MD model, atoms are represented by point masses that interact via an empirical potential function that is typically a function of bond lengths and angles; in the case of Si, a three-body or many-body potential, rather than a pair potential, is required to model the stable diamond lattice and to account for the bulk crystal properties. The trajectories of the atoms are obtained by numerical integration of Newton""s laws, where the forces are obtained from the analytical derivative of the potential function. Thus, MD provides a far more realistic description of the collision processes than BCA, but at the expense of greater computational requirements. The present invention provides a high efficiency MD process that is optimized to calculate the concentration profiles of ions implanted into crystalline substrates such as silicon (Si), gallium arsenide (GaAs), and the like.
Various objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.
In accordance with the purposes of the present invention, as embodied and broadly described herein, a computer-implemented molecular dynamics-based process simulates a distribution of ions implanted in a semiconductor substrate.
(a) The properties of the semiconductor substrate are initialized and ion dose is simulated, including an initial set of splitting depths to produce an equal number of virtual ions stopped in each interval between splitting depths.
(b) A first ion is input with selected velocity onto an impact position of the substrate and a first domain is initialized for the first ion during a first timestep, where the first domain includes all atoms of the substrate that exert a force on the ion and neighbor atoms.
(c) A first position of the first ion is determined after the first timestep.
(d) A second domain of the first ion at the first position is formed.
(e) A determination is made if the first ion has passed through a splitting depth.
(1) If not, the velocity into the substrate of the first ion is determined and a second timestep is initiated.
(2) If so, the first ion is split into first and second virtual ions, a new velocity into the substrate of the first virtual ion is determined after the first timestep and a second timestep is initiated with the first virtual ion.
(f) The first virtual ion is then set as the first ion, if created; the second timestep is set as the first time step; and the second domain is set as the first domain.
(g) Steps (c)-(e) are repeated and the second virtual ions created at each splitting interval are recorded until the first ion comes to rest and a second virtual ion is recorded as the deepest split ion.
(h) Steps (c)-(g) are repeated where the deepest split ion becomes the first ion until all of the ions resulting from splitting of the first ion come to rest.
(i) Steps (b)-(h) are then repeated until all of the ions in the ion dose to be simulated have come to rest.